Under the multipath scenario [1]}, the resultant IRS reflection
optimization problem is non-convex, and obtaining the global optimal
solution is in general intractable. As such, we adopt a compromised approach.
Considering practical delay-power spectral density in sparse channels, the first arrival path usually contains the most power of the channel due to short propagation distance [2]}. In other words, the channel gain is mainly determined by the first path. Motivated by such an observation, we formulate the worse-case optimization problem for maximizing the minimum channel gain over the first path among all devices, which is given by [3]}
\(&\mathop {\max }\limits _{\lbrace \mathbf {v}_L\rbrace }\mathop {\min }\limits _{ k \in [1,K]} \frac{\varrho ^2}{16\pi ^2d_{\mathrm {DR},k}^2d_{\mathrm {RB}}^2}\left|\mathbf {a}^H_\mathrm {R}(\phi _1^k,\psi _1^{k})\text{diag}(\mathbf {a}_\mathrm {R}(\bar{\phi }_1,\bar{\psi }_1))\mathbf {v}_L\right|^2\nonumber \\&\mathrm {s.t.}~~~[\mathbf {v}_L]_n=1,n=1,\cdots ,N,\) 
